Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-4y &= 3 \\ -3x-2y &= -1\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-3x = 2y-1$ Divide both sides by $-3$ to isolate $x$ $x = {-\dfrac{2}{3}y + \dfrac{1}{3}}$ Substitute this expression for $x$ in the first equation. $-5({-\dfrac{2}{3}y + \dfrac{1}{3}}) - 4y = 3$ $\dfrac{10}{3}y - \dfrac{5}{3} - 4y = 3$ Simplify by combining terms, then solve for $y$ $-\dfrac{2}{3}y - \dfrac{5}{3} = 3$ $-\dfrac{2}{3}y = \dfrac{14}{3}$ $y = -7$ Substitute $-7$ for $y$ in the top equation. $-5x-4( -7) = 3$ $-5x+28 = 3$ $-5x = -25$ $x = 5$ The solution is $\enspace x = 5, \enspace y = -7$.